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Tuesday, August 14, 2007

Hans-Christian ØrstedUnification of the fundamental forces is one of the big, recurring themes of theoretical physics: How to merge gravity with the rest of the standard model of particle physics? What is the GUT for the strong and electroweak force? Salam, Glashow and Weinberg were awarded the Nobel prize for the unification of electromagnetism with the weak interaction. We take so much for granted the idea that there should be a unified description of the forces of nature that it's hard to imagine that when physics started to be the science we know today, even electricity and magnetism were considered as completely disparate phenomena.

In April 1820, Hans-Christian Ørsted, professor at Copenhagen University, prepared an experiment he wanted to demonstrate to the students in his lecture class. His intention was to show how an electric current through a wire, created by the electric voltage supplied by a Volta-type pile, heats up the wire and lets it glow. By chance, a magnetic compass was standing close to the wire, and Ørsted noted that the needle of the compass was deflected when the current was switched on. Ørsted was magnetised. He didn't have time to have a closer look at this phenomenon immediately, but three months later, he sent a detailed four-page report about his discovery, written in Latin, to colleagues all over in Europe, Experiments on the Effect of a Current of Electricity on the Magnetic Needle. He had found a connection between electricity and magnetism, by quite a peculiar force pointing not along the direct line connecting the current and the needle, but perpendicular to it.

Hans-Christian Ørsted and an assistant, preparing a demonstration experiment for a lecture to show how an electric current heats up a wire. By chance, there is a compass standing on the table for another demonstration, and Ørsted notes that the needle is deflected by the current. Illustration from Louis Figuier: Les merveilles de la science, ou Description populaire des inventions modernes (1867), page 713. The portrait of Ørsted above is also from this book, page 712.

Hans-Christian Ørsted was the son of a pharmacist. He studied pharmacy, chemistry, physics and philosophy at the University of Copenhagen where he became a professor in 1806. Before, he had spent three years travelling and studying in Europe. In Germany, he was deeply influenced by Johann Ritter, best known today as the discoverer of ultraviolet light. Ritter was a proponent of the German "romantic natural philosophers" of that time, who were deeply sceptical about the Baconian method of doing science by isolating and dissecting natural phenomena in experiment. Instead, these thinkers believed in a deep unity of all nature, and a balance between the attracting and repulsive aspects of a single force responsible for all phenomena. a physicist who believed there was a connection between electricity and magnetism. As Ritter, Ørsted had speculated that galvanism and magnetism had one common cause in the motion of some fluid. Hence, in fact, Ørsted was not completely surprised by his discovery, since he had thought much about such a relation before.

Ørsted was a man with many facets. As a professor in Copenhagen, he continued his research with electric currents and acoustics, developed a comprehensive physics and chemistry program for the University, established new laboratories, and discovered the element aluminium. But he was also interested in language and literature, wrote poems, and was a close friend to Hans-Christian Andersen, the author and poet most famous for his collection of fairy tales.

Hans-Christian Ørsted was born 230 year ago today, on August 14, 1777.

Skål, Hans-Christian Ørsted!

There is a beautiful web site about Ørsted, albeit in French, L'expérience de Hans-Christian Œrsted (1820), with biographical details, information about the experiment and its reception, and scans of Ørsted's original Latin report, Experimenta circa effectum conflictus electrici in acum magneticam, as well as the English and French translations, published as Experiments on the Effect of a Current of Electricity on the Magnetic Needle (Annals of Philosophy 16 (1820) 273-277) and Expériences sur l'effet du conflict électrique sur l’aiguille aimantée (Annales de chimie et de physique 14 (1820) 417-425), respectively.

More background about the German tradition of "Naturphilosophie" in the early theories on electricity, including Ritter and Seebeck, can be found in The Form and Function of Scientific Discoveries, the Dibner Library Lecture by Kenneth L. Caneva at the Smithsonian Institution Libraries, November 2000

A detailed account of the circumstances of the discovery of electromagnetism by Ørsted is given in (subscription required) Chance in Science: The Discovery of Electromagnetism by H.C. Oersted by Nahum Kipnis, Science and Education 14 (2005) 1-28, doi: 10.1007/s11191-004-3286-0.

Electromagnetism is indeed the good word, and Oersted was the first, I think, to see a bit of the unity underlying the phenomena. Electricity and magnetism are two faces of the same phenomenon when you look at them from a physical standpoint.

The air gap of an electric motor is populated by by electromagnetic fields (as are the rotor and stator). The momentum tranmitted between them is carried by photons (so-called virtual photons) of the electromagnetic field.

Apologies that our server is down again so some of the pics are missing. They should reappear soon.

Klaus,

The electric and the magnetic field belong together. They transform into each other under a Lorentz transformation. Saying a field is purely electric doesn't even make sense without specifying the reference frame. A moving electron causes a magnetic field (think about a current in a wire). So viel 'Zur Elektrodynamik bewegter Körper'...

If space wasn't three-dimensional, how would EM work out? I am fascinated by extrapolation of EM (and other physical laws) to other dimensions. One note: we can have magnetic fields with big-dimensions N <> 3, just need a math adjustment. B isn't a vector anymore, but then again, angular momentum can't be either.) I explored this issue, and summarized in the linked blog. Basically:The average field along a charge’s axis of oscillation must equal that from a resting charge, in order to prevent uncorrected, sustained unequal reactions between charges. That obligation entails (under extrapolation to N <> 3 with all the different effects taken into account) that electric field be constant or vary as inverse square, and thus (via Gauss) N must equal one or three. The inertia of electromagnetic mass rules out the one-dimensional case.

BTW the first extrapolation is tricky, since it isn't enough just to generalize Gauss' Law (so E = kqr^(1-N).) You have to know how to wrangle the projected field retardations and strengths etc., which also invokes Lorentz contraction of the surrounding field, the Doppler-shifted intervals of interaction, etc.

Is the word "electromagnetism" really a good word to discribe the phenomena? Or does the name itself influence our thinking, because the very word dictates unity?

hm, maybe it "dictates" unity for us today, since we are used to it - but I would not go so far as to insist on "dictate".

Moreover, Ørsted himslf used his notion "electromagnetic" in a little different manner - see Caneva's text:

In his first Danish-language discussion of that work, he interpreted the new relationships by invoking an echo of his notion of form of action: "What we here a moment ago called electricity is not so in the word's stricter meaning; for the force that in the open galvanic or electric circuit acted in a distinctive manner - under a different form - that we call the electric or galvanic, acts here under an entirely different form that we most appropriately call the magnetic; meanwhile, since magnetism acts under the form of a straight line …[while] the forces here … flow incessantly into each other and form a circular course, the author has called the action dealt with here electromagnetism." It thus appears that for Ørsted the principal need for a new term stemmed from the unprecedented circular form of the electromagnetic action and not so much from the fact that it represented an interaction between electricity and magnetism.

First of all, Bee, I just wanted to say I am a big fan of your blog. Secondly, in response to Neil', (Bee probably knows this stuff better than I do), the formulation of electromagnetism through differential forms is applicable to any dimension. In it however, (after a 3+1 split) the magnetic field is not a vector field, but a two-form (which can be transformed into a one form by using the spatial hodge star operator and thence into a vector field by the metric-induced duality between one-forms and vector fields). It will remain a 2-form for any spatial dimension, but I do not see right away any means of canonically transforming it back to a vector field (since its hodge dual will not be a one form). Am I terribly mistaken?

I agree with Hag above. If you understand electrodynamics as a U(1) gauge group, there's nothing special with having 3 spatial dimensions (unless you consider self-duality or something), so one can write down a Lagrangian. # of possible photon polarizations changes however, e.g. in 1+1 there's no way a field can be orthogonal to another, so it's kind of a weird construction - I don't know the details and I'm not interested enough to look into it, since we evidently have more than 1 dimension. I have actually no idea what you are arguing above, are you talking about the n-dim. Poission equation?

Well, my main point was about another issue of physical consistency and not magnetic field generalization at all, but thanks for the helpful discussion. I got different points mixed up in one post, and my statement about magnetic field was separate. First: Sure, B and the familiar effects can be generalized to N-dimensional space, and has to be. For example, a current in 2-D is surrounded by a B-field of points. Velocity "cross" point gives you the force on a moving charge. In 4-D space xyzw: a current along x axis has a B-form let's call it, that is a yz plane when mutually perp. to the connecting w axis and zw when mutually perp. to the z axis, etc. A charge moving parallel in x direction cross-products (the generalization, is that wedge?) the yz, and force is thus along w, etc. so charge can be attracted or repelled by the wire as needed for relativity of electric field. And so on for any N. (But magnetic monopoles get silly if N <> 3. Well they don't make sense here anyway, what with loose A-field tatters trailing along....) OK, no big deal. (Cute related point: in N-space, we can have multiple rigid rotations of mutually perpendicular planes. So in xyzw, the xy plane of a rigid hypersphere can rotate at one rate, and the zw plane can rotate at another. Makes for strange days on hyperplanets...)

But my second point was, no connection to magnetism: If N <> (1 or 3), the average E field projected along the axis of oscillation of a charge is not the same as if the charge were at rest. That would allow construction of reactionless propulsion, violating conservation laws (it takes some fiddling to assure yourself things would go wrong in such a case.) N = 1 doesn't work, because of the infinite potential energy between charges, which leaves 3 as the only viable option. (See more at name link.)

I suppose there are no hints of any one else noticing this before Orsted?

I am not really an expert on this, and would have to check out more closely - but according to this French website about Oersted, it had been known before that thunderstorms and lightnings can have an influence on the magnetic needle of an compass - this effect is described in the Encyclopédie by Diderot and d'Alembert.

However, exacly how this tentative connection between electricity and magnetism could look like, and how it would work in detail, was unknown before Oersted.

But we should keep in mind that before the invention of the Volta pile around 1800, it was nearly impossible to create stable electric direct currents to do experiments with...

the theory of electromagnetism is a wonderful topic to tackle with the calculus of forms - that's what Hag and Bee have mentioned. If you do this, you can work out how the magnetic field (components of a two-form, which corresponds to a pseudovector in three space dimension) would "look like" in more than three dimensions. In two, its a scalar. If you are interested in this, you may find the text by Bamberg and Sternberg helpful, and some of the papers by Hehl and Obukhov. But now from your last comments, I guess you know all that and are heading in another direction...